A common solution to this which may or may not work for you is to use a centrifugal clutch.

Off the shelf options would be too large for your application; and they wouldn't kick in until too high an rpm. But you may be able to 3D print something based on this principal.

I'm thinking very heavy arms on the inner shaft. Plus teeth or "ledges" on the outer drum and arms so that once it catches it will never slip.

A common solution to this which may or may not work for you is to use a centrifugal clutch.

Off the shelf options would be too large for your application; and they wouldn't kick in until too high an rpm. But you may be able to 3D print something based on this principal.

If you make the arms very heavy, with light springs it will work at lower rpms. You could also replace the friction element with teeth or a pawl style mechanism so that once it's engaged it will never slip.